The German weekly said on Sunday that Israeli intelligence and at least one other secret service intercepted Kerry’s phone calls during a doomed, nine-month effort to broker a peace deal.

If confirmed, the report will further sour the diplomat’s relationship with Binyamin Netanyahu’s government and raise fresh questions about the vulnerability of phone communications to eavesdropping.

There was no immediate reaction from Jerusalem or Washington. The State Department did not respond to a request for comment.

The report was published on another bloody day in Gaza, where a projectile hit a street outside a school where people were sheltering, killing at least seven and wounding dozens, many of whom were buying sweets and biscuits from stalls.

The UN secretary general, Ban Ki-moon, called the attack a “moral outrage and a criminal act” and said the Israel Defence Forces had been repeatedly informed of the location of civilian shelters.

Citing “several intelligence sources”, Der Spiegel said Israeli spies and an unidentified intelligence agency listened in on Kerry’s talks with high-ranking officials from Israel, the Palestinian territories and Arab states. Some calls were allegedly made on normal phones and were not encrypted.

“The government in Jerusalem then used the information obtained in international negotiations aiming to reach a diplomatic solution in the Middle East,” it said.

Kerry invested his authority in the ambitious attempt to relaunch moribund Middle East diplomacy last year and persuaded Netanyahu and the Palestinian president, Mahmoud Abbas, to resume negotiations. The effort fizzled out in April, with each side accusing the other of bad faith.

Kerry made several publicly reported comments during the talks that frayed his relationship with Jerusalem. He warned that Israel risked becoming an “apartheid state” if it did not reach a peace deal with the Palestinians, prompting protests by Israeli and US politicians. Kerry apologised.

The secretary of state ignited another furore by warning that failure to reach a peace agreement would damage Israel’s capacity to be a democratic state and could lead to more boycotts.

Israel’s defence minister, Moshe Ya’alon, called Kerry “obsessive and messianic” in his pursuit of an agreement. Yuval Steinitz, Israel’s intelligence minister, called his comments “offensive, unfair and insufferable”.

Two weeks ago, Kerry, who was making a tour of the US Sunday talk shows, was recorded by an open Fox News microphone appearing to criticise Israeli claims of a measured approach to its strikes on Gaza. “It’s a hell of a pinpoint operation, it’s a hell of a pinpoint operation,” Kerry said, while on the phone to an aide.

That Israel would wish to eavesdrop on its envoy is unlikely to surprise Washington but the allegation that it succeeded, along with another intelligence agency, may raise alarm.

US intelligence agencies are acutely aware of communication vulnerabilities – and are presumed to take countermeasures – given that they themselves tapped the phone of the German chancellor, Angela Merkel, among others.

The whistleblower Edward Snowden’s revelations about National Security Agency snooping on foreign leaders as well as millions of ordinary Americans makes it awkward for Washington to respond to reports of foreign intelligence agencies – be they Chinese, Israeli or anyone else – spying on US officials and corporations.

In May, Newsweek reported “unrivalled and unseemly” Israeli espionage in the US under cover of trade missions and joint defence technology contracts. Israeli officials called the report false and malicious.

It was reported in March that Israel and the Washington were discussing the possible release of the spy Jonathan Pollard, who is serving a life sentence for selling US secrets to Israel in the 1980s, as part of Kerry’s efforts to keep the peace process afloat.

Sunday’s attack on the school in Gaza was the third time in 10 days that a UN school had been hit. Regional efforts to broker a diplomatic end to the fighting between Israel and Hamas have so far proved elusive; the conflict is now in its 27th day and more than 1,700 people have been killed.